The \(\)  distance was first motivated in [1]} to solve shape matching problems.
It was applied successfully in natural language processing for unsupervised translation learning [2]}, [3]}, in generative learning for objects lying in spaces of different dimensions [4]} and to build VAE for graphs [5]}.
It has been adapted for domain adaptation over different spaces [6]}.
It is also a relevant distance to compute barycenters between graphs or shapes  [7]}, [8]}.
When \((,)\)  are Euclidean spaces, this distance compares distributions up to rigid isometries, and is closely related (but not equal) to metrics defined by Procrustes analysis [2]}, [10]}.
It was successfully applied in biology to align multi-omics biology [11]}, [12]}.
